Shell Method is particularly good for calculating volume of a 3D shape by rotating a 2D shape around a VERTICAL LINE.Imagine there is a CYLINDER, and we’re to calculate the surface area of the cylinder, and integrate the surface areas when the cylinder gets thiner and thiner.
Refer to Khan academy: Shell method for rotating around vertical line?Jump to Khan academy for some practice: Shell method?Refer to Desmos Animation: Solids of Revolution (about y-axis)
?Refer to the awesome article: The shell method of finding volumes of revolution
?Refer to mathdemos.org for more intuitive animations: SHELL METHOD DEMO GALLERY
Example
Solve:
- Let?s draw it out first:
- Based on the Shell method of integrating Cylinder’s shells, we got the equation:
